1. Without his help in the war, we would have never won in the first place. He spent a lot of his money to help the patriots win the war. The patriots needed his help to win the war.
2. He was a good commander but he was never rewarded for what he did, so even if he joined the British later, It is understandable that he would rather join the enemy than to not get credit for his hard work.
3. The patriots stopped rewarding him even after he did better at helping them win, that was most likely unfair to him and I would not be surprised if he was tired of the patriots not doing anything to show that they were grateful for his work. He deserved better than this!
So there